摘要
通过Halpin-Tsai模型来预测功能梯度石墨烯纳米增强复合材料(functionally graded multilayer graphene nanoplatelets reinforced composite,FG-GPLRC)板的有效弹性模量,并根据混合律确定板的质量密度和泊松比。进一步基于一阶剪切变形板理论和四边形四节点等参元建立用有限元方法求解计算的模型来分析该复合结构的自由振动特性,通过与文献结果对比验证了方法的有效性和可靠性。研究表明,在聚合物板中掺入少量(质量占比g=1%)石墨烯纳米片(graphene nanoplatelets,GPLs)就可使板的自振频率提高1倍。选用表面积更大、厚度更薄的GPLs可更有效地增强聚合物板,且应尽量选用正方形的GPLs。而在板的顶层和底层掺入更多GPLs可提高增强效率,但该模式下参数变异性对动力特性的影响也较大。GPLs的弹性模量、质量密度对自振频率的影响大于基体材料的相应参数。固支边界时板的频率较高而一边固支三边自由时频率较低,而不同边界条件下各材料参数对自振频率的影响规律接近。
The Halpin-Tsai model was adopted to determine the Young s modulus of the functionally graded multilayer graphene nanoplatelets reinforced composite(FG-GPLRC)plates,and the rule of mixture was used to calculate the Poisson s ratio and mass density of the FG-GPLRC plate.According to the theories of first-order shear deformation plate and quadrilateral four-node isoparametric element,a finite element method was established for analyzing the free vibration of the FG-GPLRC plate.The validity and accuracy of the proposed method were verified by comparing with the available reported results.It is shown that adding of a very small amount of GPLs(weight fraction g=1%)can double the natural frequency of the FG-GPLRC plate.Square-shaped GPLs with larger surface area and fewer graphene layers produce better reinforcement.Dispersing more GPLs near the top and bottom surfaces of plate can improve the reinforcement efficiency but increase the sensitivity of natural frequency to parameters of materials.Comparing with the polymer matrix,the Young s modulus and mass density of graphene affect the natural frequency more significantly.The plate fixed on four sides has larger natural frequency than the plate only fixed on one side,while the effects of material parameters on natural frequency are similar under various boundary conditions.
作者
罗东晖
黄友钦
杨振宝
LUO Dong-hui;HUANG You-qin;YANG Zhen-bao(Guangzhou University-Tamkang University Joint Research Center for Engineering Structure Disaster Prevention and Control,Guangzhou University,Guangzhou 510006,China)
出处
《科学技术与工程》
北大核心
2020年第26期10674-10682,共9页
Science Technology and Engineering
基金
国家自然科学基金(51208126,51778161)。
关键词
功能梯度石墨烯增强复合板
自由振动
有限元方法
参数分析
functionally graded graphene reinforced composite plates
free vibration
finite element method
parametric analysis
